Guides / The missing denominator
Should one horror story change your mind?
In brief
Because a single vivid case is a sample of one, and a sample of one cannot tell you a rate. Amos Tversky and Daniel Kahneman handed people a hypothetical: a witness, four times out of five reliable, says the hit-and-run cab was Blue. Most people believed the witness and stopped there. The story only means something once you know how many stories there are. Ask for the denominator before the one loud case decides for you.
The cab that ran#
Picture a cab at night. Tires screech, a shape pulls away, no plate number caught. A witness steps forward and says the cab was Blue. The city runs two companies: eighty five cabs in a hundred belong to Green, fifteen belong to Blue. The court tests the witness under conditions matching that night and finds the same result each time it tries: right four times in five, wrong the fifth.
Two psychologists, Amos Tversky and Daniel Kahneman, handed this exact puzzle to hundreds of people starting in the 1970s, and the answers came back almost uniform: eighty percent chance the cab was Blue. Look closely and that number is a coincidence with a cause. It matches the witness’s own reliability exactly, repeated back with the color swapped in, as though the city’s cab ratio played no part in the answer at all.
Run the two facts together instead of letting one erase the other and the picture changes. Fifteen Blue cabs in a hundred to start. The witness catches the truth eight times in ten and misses two. Weight the rare color by how rarely it shows up, fold in the four-out-of-five witness, and the odds land near twelve to seventeen, a probability close to forty one percent. Even with a witness pointing a finger, green remains the likelier color of the car that fled.
The story does the arguing#
Maya Bar-Hillel ran the puzzle again in 1980 and noticed something almost funny. People who missed it, asked about their answer afterward, vehemently defended their witness-based judgment, denying that the cab distribution should have had anything to do with their answer
. The mistake never felt like a mistake. It felt like common sense.
Here is the detail that turns this from a joke about bad math into something sharper. Take the exact same puzzle and remove the witness entirely, leave only the plain fact that Green cabs outnumber Blue nearly six to one, and ask the same people for the odds. They answer fifteen percent, almost every time, dead on the true rate. The denominator was never beyond anyone’s reach. It loses, every time, only when a specific, confident, human voice is standing right beside it.
The fix was never to throw the witness out. A witness who is right four times in five is worth hearing. The fix keeps the testimony exactly where it stands and seats the rate right beside it, so the two get read together instead of one erasing the other. Story plus rate, combined rather than traded, is the whole of what this guide is asking you to build into a habit.
Shrinking the one dot#
Draw the same idea as dots instead of cabs. One dot, filled and loud, is the one story that reaches you first: a friend’s warning, a single scorched review, the account that went everywhere. The slider sets how many people actually stand behind it. Drag it upward and watch the one dot keep its identity while its true share of the field shrinks toward the truth.
At ten counted, the one dot is nearly the whole picture, and the gut reads it as almost the whole truth. At one thousand, the same dot is a speck lost in a field it once seemed to define, and the honest reading is a fraction so small the eye has to hunt for it. The story never changed. Only the denominator did, and the denominator was the part that was actually missing.
One story, out of how many#
Leave the puzzle behind and open a real feed of reviews. One post says a fee showed up that a company swore would never appear. One thread says a refund that was promised never arrived. The account is specific, dated, and often true on its own terms. What it cannot tell you, standing alone, is the rate: out of everyone who dealt with that company, how many lived through the same thing.
A Nolemy record built around the claim Uber Eats refunds missing items
exists for exactly this reason. It holds fifty six separate reports across nine platforms: a rider on X refunded £3.06
against an item that cost £6.99
, a Trustpilot reviewer counting 3 orders with incorrect and missing items and 0 refunds
. Read only the loudest of those alone and the company looks like it never refunds anyone. Read the full fifty six and a narrower, stranger pattern appears: refunds do arrive, then shrink, then stop, usually within the first two claims.
This is the reflex worth building. Whenever one account is doing all the arguing, the honest next question is never whether the account is true. It is how many accounts exist that you have never read. A Nolemy record is one answer to that question, counted and dated instead of guessed at, so the one story you saw stops standing in for a population it was never big enough to represent.
“Uber Eats refunds missing items”
56 reports · 9 platforms · the count behind the one story · signed be14 0a84 dcc7 b842
The objection#
Amos Tversky & Daniel Kahneman, “Evidential Impact of Base Rates” (technical report, 15 May 1981), hosted copy, later the title chapter of Judgment under Uncertainty: Heuristics and Biases (Cambridge University Press, 1982). Maya Bar-Hillel, “The base-rate fallacy in probability judgments,” Acta Psychologica 44 (1980), PDF. Jonathan Koehler’s 1996 reconsideration, summarized in Eamon Fulcher’s case-study chapter, PDF. The Nolemy record on Uber Eats refund denials, cited in full below. All fetched 18 July 2026.